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arXiv · 2108.02828

Rank $r$ DT theory from rank $1$

Soheyla Feyzbakhsh·Richard P. Thomas
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Abstract

Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r$ on $X$ in terms of those counting sheaves of rank 1. By the MNOP conjecture they are therefore determined by the Gromov-Witten invariants of $X$.

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Soheyla Feyzbakhsh, Richard P. Thomas. 2021-08-05. Rank $r$ DT theory from rank $1$. https://doi.org/10.1090/jams/1006

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